GCF of 8385/574, 7865/6860
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8385/574, 7865/6860 i.e 65/281260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8385/574, 7865/6860.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 8385/574,7865/6860?
Given fractions are 8385/574,7865/6860
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 8385/574,7865/6860, numerators are 8385,7865
Denominators are 574,6860
The GCF of 8385,7865 is 65 .
LCM of 574,6860 is 281260.
The greatest common factor of 8385/574,7865/6860 = [GCF of 8385,7865]/[LCM of 574,6860]= 65/281260
Therefore, the GCF of 8385/574,7865/6860 is 65/281260.
To find the highest common factor of 8385,7865, we have to find the factors of both numbers and list the highest common factor.
The factors of 8385 are 1, 3, 5, 13, 15, 39, 43, 65, 129, 195, 215, 559, 645, 1677, 2795, 8385
The factors of 7865 are 1, 5, 11, 13, 55, 65, 121, 143, 605, 715, 1573, 7865
The HCF of 8385,7865 is 65.
Lets's calculate GCF of 8385,7865
| 5 | 8385, 7865 |
| 13 | 1677, 1573 |
| 129, 121 |
∴ So the GCF of the given numbers is 5 x 13 = 65
Greatest Common Factor of 8385,7865 By Matching Biggest Common Factor Method
Now, list down the factors of 8385
:1,3,5,13,15,39,43,65,129,195,215,559,645,1677,2795,8385
Now, list down the factors of 7865
:1,5,11,13,55,65,121,143,605,715,1573,7865
Greatest Common Factor
We found the factors 8385,7865 . The biggest common factor number is the GCF number.
So the greatest common factor 8385,7865 is 65.
Lets's calculate LCM of 574,6860
| 2 | 574, 6860 |
| 7 | 287, 3430 |
| 41, 490 |
∴ So the LCM of the given numbers is 2 x 7 x 41 x 490 = 281260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 65/281260
Therefore, the GCF of Fractions 8385/574,7865/6860 is 65/281260
Least Common Multiple of 574,6860 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 574,6860 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(574,6860) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(574,6860) x common factors =14 x 1 = 14
LCM(574,6860) = ( 574 × 6860 ) / 14
LCM(574,6860) = 3937640 / 14
LCM(574,6860) = 281260
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FAQs on GCF of Fractions of 8385/574, 7865/6860
1. What is the HCF of 8385,7865?
The HCF of 8385,7865 is 65
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 8385/574, 7865/6860?
Answer: GCF of Numerators as per given numbers 8385/574, 7865/6860 is
GCF of Numerators i.e. for 8385,7865 is 65
LCM of denominators i.e. for 574,6860 is 281260.
Thus, GCF of Fractions is 65/281260.Finally, GCF of Fractions for 8385/574, 7865/6860 is 65/281260.